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Ben wants his savings of R40,000 to earn him interest of R2000 at Fatala bank IF Fatala bank changes the rate of interest to 7% how long must Ben save?

Mathematics

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Answer

2.8125 years\text{2.8125 years}

Step-by-step solution

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Ben wants his savings of 40,000 to earn interest of 9000 at Faida bank. If Faida bank charges interest at the rate of 8% how long must Ben save?

  1. Identify the given values for simple interest.

    The principal amount (P) is Ksh 40,000\text{Ksh } 40,000.
    The interest (I) earned is Ksh 9,000\text{Ksh } 9,000.
    The annual interest rate (R) is 8%8\%, which is 0.08 as a decimal.
    We need to find the time (T) in years.

  2. Use the simple interest formula I=P×R×TI = P \times R \times T.

    Substitute the known values into the formula:

    9000=40000×0.08×T9000 = 40000 \times 0.08 \times T

  3. Solve for T.

    First, multiply P and R:

    9000=(40000×0.08)×T9000 = (40000 \times 0.08) \times T 9000=3200×T9000 = 3200 \times T

    Now, divide both sides by 3200:

    T=90003200T = \frac{9000}{3200} T=9032T = \frac{90}{32} T=4516T = \frac{45}{16} T=2.8125 yearsT = 2.8125 \text{ years}

    Ben must save for 2.8125 years.

    2.8125 years\text{2.8125 years}
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